jagomart
digital resources
picture1_Processing Pdf 180393 | 01 Intro


 156x       Filetype PDF       File size 2.05 MB       Source: willett.psd.uchicago.edu


File: Processing Pdf 180393 | 01 Intro
1 elements of statistical signal processing ece 830 spring 2017 1 31 what do we have here the rst step in many scientic and engineering problems is often signal analysis ...

icon picture PDF Filetype PDF | Posted on 30 Jan 2023 | 2 years ago
Partial capture of text on file.
       1: Elements of Statistical Signal Processing
                       ECE 830, Spring 2017
                                                               1/31
  What do we have here?
       The first step in many scientific and engineering problems is often
       signal analysis. Given measurements or observations of some
       physical process, we ask the simple question “what do we have
       here?” For instance,
         ◮ Is there any information in my measurements, or are they just
            noise?
         ◮ Is my signal in category A or B?
         ◮ What is the signal underlying my noisy measurements?
       Answering this question can be particularly challenging when
         ◮ measurements are corrupted by noise or errors
         ◮ the physical process is“transient” or its behavior changes over
            time.
                                                                             2/31
  Fourier analysis
       In some contexts, these challenges can be addressed via Fourier
       analysis, one of the major achievements in physics and
       mathematics. It is central to signal theory and processing for
       several reasons.
       Recall the Fourier series:
                                      ∞
                             x(t) = X cke−j2πfkt.
                                    k=−∞
       This is used for
         ◮ analysis of physical waves (acoustics, vibrations, geophysics,
            optics)
         ◮ analysis of periodic processes (economics, biology, astronomy)
                                                                             3/31
  Fourier analysis and filtering
       Recall the Fourier transform
                                   Z ∞        −j2πft
                           X(f)=         x(t)e      dt
                                     −∞
       and the convolution integral
                         y(t) =Z ∞ h(τ)x(t−τ)dτ
                                 −∞
                                Z ∞              j2πft
                              =      H(f)X(f)e        df
                                 −∞
       which describes, for example, the result of sending a signal x
       through a filter h. Two key facts:
         ◮ Convolution in time ⇐⇒ multiplication in frequency
         ◮ A stationary, zero-mean, Gaussian random process can be
            represented as a white noise process passed through a linear,
            time-invariant filter
                                                                            4/31
The words contained in this file might help you see if this file matches what you are looking for:

...Elements of statistical signal processing ece spring what do we have here the rst step in many scientic and engineering problems is often analysis given measurements or observations some physical process ask simple question for instance there any information my are they just noise category a b underlying noisy answering this can be particularly challenging when corrupted by errors transient its behavior changes over time fourier contexts these challenges addressed via one major achievements physics mathematics it central to theory several reasons recall series x t cke j fkt k used waves acoustics vibrations geophysics optics periodic processes economics biology astronomy ltering transform z ft f e dt convolution integral y h d df which describes example result sending through lter two key facts multiplication frequency stationary zero mean gaussian random represented as white passed linear invariant...

no reviews yet
Please Login to review.